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The intersection Fl of the Gergonne line and the Soddy line. In the above figure, D^', E^', and F^' are the Nobbs points, I is the incenter, Ge is the Gergonne point, and S ...

Let M^n be an n-manifold and let F={F_alpha} denote a partition of M^n into disjoint pathwise-connected subsets. Then F is called a foliation of M^n of codimension c (with ...

A set of algebraic invariants for a quantic such that any invariant of the quantic is expressible as a polynomial in members of the set. Gordan (1868) proved the existence of ...

The internal (external) bisecting plane of a dihedral angle of a tetrahedron divides the opposite edge in the ratio of the areas of the adjacent faces.

An orientation of an undirected graph G is an assignment of exactly one direction to each of the edges of G. Only connected, bridgeless graphs can have a strong orientation ...

The polyhedron compound of the great icosahedron (U_(53)) and the small stellated dodecahedron (U_(34)), sometimes known as the great cid. Four faces meet at each edge of the ...

The great snub dodecicosidodecahedron is the uniform polyhedron with Maeder index 64 (Maeder 1997), Wenninger index 115 (Wenninger 1989), Coxeter index 80 (Coxeter et al. ...

There does not exist an everywhere nonzero tangent vector field on the 2-sphere S^2. This implies that somewhere on the surface of the Earth, there is a point with zero ...

A triple (a,b,c) of positive integers satisfying a<b<c is said to be harmonic if 1/a+1/c=2/b. In particular, such a triple is harmonic if the reciprocals of its terms form an ...

A clause (i.e., a disjunction of literals) is called a Horn clause if it contains at most one positive literal. Horn clauses are usually written as L_1,...,L_n=>L(=¬L_1 v ... ...